TY - JOUR

T1 - Brusselator

T2 - An abstract chemical reaction?

AU - Lavrova, A. I.

AU - Postnikov, E. B.

AU - Romanovsky, Yu M.

PY - 2009/12/1

Y1 - 2009/12/1

N2 - In this paper we consider the Brusselator and the Sel'kov model, which describes the irreversible reaction of glycolysis in the regime of self-sustained oscillations. We show that these two differently constructed models can be reduced to a single equation - a generalized Rayleigh equation. The physical basis for this generality is investigated. The advantages of this equation as a tool for qualitative and quantitative analyses, as well as the similarities and differences of the solutions realized for each of the two concrete models in the cases of almost harmonic and relaxation self-sustained oscillations, are discussed.

AB - In this paper we consider the Brusselator and the Sel'kov model, which describes the irreversible reaction of glycolysis in the regime of self-sustained oscillations. We show that these two differently constructed models can be reduced to a single equation - a generalized Rayleigh equation. The physical basis for this generality is investigated. The advantages of this equation as a tool for qualitative and quantitative analyses, as well as the similarities and differences of the solutions realized for each of the two concrete models in the cases of almost harmonic and relaxation self-sustained oscillations, are discussed.

UR - http://www.scopus.com/inward/record.url?scp=78650930573&partnerID=8YFLogxK

U2 - 10.3367/UFNe.0179.200912h.1327

DO - 10.3367/UFNe.0179.200912h.1327

M3 - Article

AN - SCOPUS:78650930573

VL - 52

SP - 1239

EP - 1244

JO - Physics-Uspekhi

JF - Physics-Uspekhi

SN - 1063-7869

IS - 12

ER -